A music video to accompany the release of "Baby Come Home" was directed by Lorenzo Fonda and first released onto YouTube on May 30, 2012 at a total length of three minutes and fourteen seconds. The video shows the band members dress up as a variety of characters. Jake Shears can be seen as a nun and knight in scenes, while Ana Matronic becomes a sailor and a witch.
Lewis Corner of Digital Spy gave the song a positive review stating:
As such, we breathed a sigh of relief when the four-piece confirmed 'Baby Come Home' as their next single. Partly because its mix of bouncy piano and funky guitar is more addictive than a game of Temple Run, but mainly because it recalls classic Scissor Sisters circa 2004. It's a welcome reminder of their roots and one that deserves to replicate some of their heyday success. .